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--- b:head_first_statistics:calculating_probability [2020/09/29 14:59] – hkimscil
+++ b:head_first_statistics:calculating_probability [2023/09/26 20:06] (current) – [Dependent and Independent event] hkimscil
@@ Line 30: / Line 30: @@
 A = event A
-[{{:b:head_first_statistics:pasted:20190924-173343.png|7이 일어나는 경우  }}]
+[{{:b:head_first_statistics:pasted:20190924-173343.png?850|7이 일어나는 경우  }}]
 <WRAP clear />
-[{{:b:head_first_statistics:pasted:20190924-173810.png|일반화  }}]
+[{{:b:head_first_statistics:pasted:20190924-173810.png?650|일반화  }}]
 <WRAP clear />
@@ Line 90: / Line 90: @@
 [{{:b:head_first_statistics:pasted:20190924-181909.png?400}}]
 <WRAP clear />
-[{{:b:head_first_statistics:pasted:20190926-105816.png| }}]
+[{{:b:head_first_statistics:pasted:20190926-105816.png?800| }}]
   * Intersection $ \cap $
@@ Line 137: / Line 137: @@
-[{{:b:head_first_statistics:pasted:20190924-191720.png?550}}]
+[{{:b:head_first_statistics:pasted:20190924-191720.png?800}}  ]
-[{{:b:head_first_statistics:pasted:20190924-191951.png?550}}]
+[{{:b:head_first_statistics:pasted:20190924-191951.png?800}}  ]
@@ Line 149: / Line 149: @@
 <wrap>''3/4, 1/4, 2/5, 3/5, 1/3, 2/3''</wrap>
-[{{:b:head_first_statistics:pasted:20190926-111825.png?550|Donuts Buying at Doncun}}]
+[{{:b:head_first_statistics:pasted:20190926-111825.png?650|Donuts Buying at Doncun}}  ]
-[{{:b:head_first_statistics:pasted:20190926-112041.png?550|Probability, conditional}}]
+[{{:b:head_first_statistics:pasted:20190926-112041.png?650|Probability, conditional}}  ]
 <WRAP clear />
@@ Line 160: / Line 160: @@
   * P(Coffee)
   * P(Donuts | Coffee)
+<code>
+ d (3/4) --  c [x = 3/5] [k = p(c and d)]
+         -- ~c [y = 2/5]
+~d (1/4) --  c (1/3) --> [a = p(c and ~d)]
+         -- ~c [2/3]
+x * 3/4 = p(d and c) = 9/20
+x = 9/20 * 4/3
+  = 36/60
+  = 6/10 = 3/5
+P(~d ∩ c) = a = 1/4 * 1/3 = 1/12
+P(c) = k + a
+k = 3/4 * 3/5 = 9/20
+a = 1/12
+P(c) = 54/120 + 10/120 = 64/120 = 16/30 = 8/15
+c (8/15) --  d [j]
+         -- ~d
+~c (7/15)
+j = p(d | c)
+p(d and c) = 9/20 이므로
+/15 * j = 9/20
+j = 9/20 * 15/8 = 9/4 * 3/8 = 27/32
+</code>
 </WRAP>
@@ Line 194: / Line 221: @@
 Step 1: Finding P(Black ∩ Even)
+\begin{eqnarray*}
+P(Black \cap Even)
+& = & \frac {18}{38} * \frac {10}{18} \\
+& = & \frac {10}{38} \\
+P(Black \vert Even) & = & \frac {P(Black \cap Even)}{P(Even)} \\
+P(Black \cap Even) & = & P(Black) * P(Even \vert Black) \\
+P(Black \vert Even) & = & \frac{P(Black) * P(Even \vert Black)} {P(Even)}
+\end{eqnarray*}
-$$ {P(Black \cap Even) = \frac{18}{38} * \frac{10}{18} = \frac{10}{38} $$
-$$ P(Black \vert Even) = \frac {P(Black \cap Even)}{P(Even)} $$
-$$ P(Black \cap Even) = P(Black) * P(Even \vert Black)$$
-$$ P(Black \vert Even) = \frac{P(Black) * P(Even \vert Black)} {P(Even)} $$
 Step 2: Finding P(Even)
@@ Line 262: / Line 291: @@
 $$P(A \vert B) = \frac {P(A) * P(B \vert A)}{P(A) * P(B \vert A) + P(A') * P(B \vert A')} $$
-This is called "<fc #ff0000>**Bayes' Theorem**</fc>"
+This is called "<fc #ff0000>**<fs large>Bayes' Theorem</fs>**</fc>"
 ====== e.g. ======
@@ Line 326: / Line 356: @@
   * The probability of the ball having landed in a pocket with a number greater than 4 given that it’s red.
   * The probability of the ball landing in pockets 1, 2, 3, or 4.
 </WRAP>
+https://youtu.be/NIqeFYUhSzU?t=904
+https://youtu.be/NIqeFYUhSzU?t=1296
+https://youtu.be/NIqeFYUhSzU?t=2550
+https://wbd.ms/share/v2/aHR0cHM6Ly93aGl0ZWJvYXJkLm1pY3Jvc29mdC5jb20vYXBpL3YxLjAvd2hpdGVib2FyZHMvcmVkZWVtLzZjMjgyZjc1Y2Y0MDRhYjA4MDk5ODAyN2Y0ODZiMjlkX0JCQTcxNzYyLTEyRTAtNDJFMS1CMzI0LTVCMTMxRjQyNEUzRF83NzZhZWUxNS0yNjNmLTQ3ZWUtYWI0My1mNDM4ZDIwYzExMTI=
+{{:b:head_first_statistics:pasted:20230926-200603.png}}